Horizons and non-local time evolution of quantum mechanical systems

TL;DR

This paper introduces a quantum horizon wave-function framework to describe the causal structure and non-local time evolution of quantum systems with horizons, using a free particle as a toy model.

Contribution

It proposes a novel approach to incorporate horizon causality into quantum state evolution via the horizon wave-function concept.

Findings

Horizon wave-function encodes causal structure of quantum states.

New evolution equations prevent signals from inside horizons.

Illustration with a free particle model demonstrates the approach.

Abstract

According to general relativity, trapping surfaces and horizons are classical causal structures that arise in systems with sharply defined energy and corresponding gravitational radius. The latter concept can be extended to a quantum mechanical state simply by means of the spectral decomposition, which allows one to define an associated "horizon wave-function". Since this auxiliary wave-function contains crucial information about the causal structure of space-time, a new proposal is formulated for the time-evolution of quantum states in order to account for the fundamental classical property that outer observers cannot receive signals from inside a horizon. The simple case of a single massive free particle at rest is used throughout the paper as a toy model to illustrate the main ideas.